Multiobjective optimization of rotor-bearing systems with an investigation of goal programming approach

With ever-increasing demand for higher flexibility and higher speeds of operation of high-speed rotating machinery, study of their unbalance responses and stability are of paramount importance. For easier maintenance and transport, weight of such systems is also a critical criterion. In the present study, optimum design parameters of a rotor-bearing system are found by employing multiple multiobjective optimization schemes for simultaneously minimizing unbalance response, maximizing stability limit speed, and minimizing system weight. This is an improvement over previous systems where simple equal weighting of multiple objective functions is carried out to reduce computational challenges. The shaft is assumed to be hollow and modeled as an assembly of 10 two-noded Euler-Bernoulli beam elements with an isotropic disc mounted on it. Genetic algorithm and its multiobjective variant (NSGA-II) are used to find the global optima. The technique of goal programming is identified as a more practical and less computationally challenging alternative to Pareto-based optimization, while yielding an approximate optimum. Complexities arising due to gyroscopic effects and dynamic nature of anisotropic fluid film bearings are also considered, along with practical upper and lower bounds of design variables and maximum von Mises stress developed in the system as constraints.